Implied cross rate and triangular arbitrage calculator

The consistency check between three quotes.

Interactive: implied cross rate and triangular arbitrageEasy

EUR/USD GBP/USD Quoted EUR/GBP

Implied cross: —
Quoted cross: —
Gap: —
Gross on $1m: —
Reading: —

In liquid majors this arbitrage was closed by machines decades ago and any visible gap is inside the spread you would actually pay — run it through the trading-cost calculator before believing it. Its lasting use is as a consistency check: a cross that will not reconcile with its two legs is usually a stale or mis-keyed quote.

The idea behind it

This calculator belongs to Foreign Exchange, where the mechanism it computes is explained step by step, with the formula, what each input means and where the simple model stops being right. Everything is computed in your browser; nothing you type is sent anywhere.

Instruments it applies to

FX Spot — Exchanging one currency for another, settled in two days — the deepest market humanity has built.
FX Forward — Lock an exchange rate for a future date — the corporate world's everyday currency hedge.
Non-Deliverable Forward — A forward for currencies you can't take home — settled in dollars against an official fixing.
FX Swap — Borrow one currency against another: the invisible funding machine underneath global finance, and the one nobody sees.
Cross-Currency Swap — Swap debt from one currency into another for years at a time — principal, interest and all.
FX Future — The exchange-traded twin of the FX forward — same economics, public prices, a clearing house instead of a credit line.
Dual Currency Deposit — A deposit with a headline rate several times the going one, which the bank may repay in a currency you did not want.

More calculators from Foreign Exchange

Forward rate & swap points (CIP) — the no-arbitrage forward.
Carry trade arithmetic — differential, leverage, breakeven.
Currency-hedged yield — what a foreign bond really pays after hedging.
Position sizing from risk — size follows risk, never the reverse.

All calculators

Not advice. This explains how something works; it is not a recommendation, and nothing here is tailored to you. You can lose everything you put in — with leveraged instruments, considerably more. StrikeAndYield is not a regulated firm and provides no financial services.

The same in full — six points, and why each one matters

No advice, no recommendation. Nothing on this page constitutes investment, financial, legal, tax or accounting advice, a personal recommendation, or an offer or solicitation to buy or sell any financial instrument.
Nothing here is tailored to you. This is written for a general audience. It does not consider your objectives, financial situation, knowledge, time horizon or tolerance for loss.
The examples are simplified. Worked examples use round numbers and leave out costs, spreads, taxes, collateral, settlement and market conventions that materially change real outcomes.
The models are teaching models. Formulas shown are standard textbook formulations. Institutions add calibration, live market data and credit, funding and capital adjustments — nothing here will reproduce a dealer’s quote or produce a valuation you can rely on.
These instruments carry risk. You can lose your entire investment. Leveraged instruments — futures, options, CFDs, perpetual futures and similar — can cost you considerably more than you originally deposited.
We are not a regulated firm. StrikeAndYield is an independent publication by DELISORIA. It is not a bank, broker, fund manager or licensed adviser, it provides no financial services, and reading it creates no client relationship. For decisions about your own money, consult a professional licensed in your jurisdiction. See the full disclaimer.